Spatial-Temporal Modeling and Computation for Physical Processes and Numerical Simulations

每一天的每一分钟，一群卫星都会捕捉到下面场景的图像，超级计算机会大量模拟未来的天气和气候，积累大量关于地球及其大气层的原始信息。由于大量的公共资金已经投入到这些数据的收集和制作中，统计工具必须能够完成分析任务。该项目旨在对这些信息进行分类，准确填补原始数据中的空白，从图像序列中推断有意义的数量-例如变化的风模式，并通过数值计算机模拟分析来完善我们对地球作为一个相互关联的系统的理解。在本项目期间开发的统计技术将通过软件的公开传播向更广泛的社区提供。学生和新兴的研究人员将接受培训，使用新的方法，并将被赋予特定的知识和独立的批判性思维技能，冒险出去，使自己的影响。该项目概述了在地球科学数据分析管道的三个关键任务的进展。(1)来自地面监测器和极地轨道卫星的观测结果往往在空间和时间上有差距，必须加以插值。因此，提出了新的高斯过程近似，其在改进近似的同时显著减少计算工作量，从而允许快速和准确的插值。(2)地球静止卫星传感器提供了对大气进行精细、连续监测的机会。该提案概述了使用这些数据的框架-这些数据由图像的时间序列组成-以推断高空风场。(3)超级计算的步伐继续提高我们产生高分辨率数值模拟的能力，这需要新的计算工具来分析输出。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Every minute of every day, a swarm of satellites captures images of the scenes below, and supercomputers churn out simulations of future weather and climate, accumulating a mountain of raw information about the Earth and its atmosphere. Since a significant amount of public funding has been devoted to the collection and production of this data, it is imperative that statistical tools be up to the task of analyzing it. This project aims to sort through this information, accurately filling in gaps in the raw data, inferring meaningful quantities--such as changing wind patterns--from sequences of images, and refining our understanding of the Earth as an interconnected system through the analysis of numerical computer simulations. Statistical techniques developed during this project will be made accessible to the broader community by public dissemination of software. Students and emerging researchers will be trained to use the new methods and will be empowered with specific knowledge and independent critical thinking skills to venture out and make their own impacts.The project outlines advancements for three crucial tasks in the geoscientific data analysis pipeline. (1) Observations from ground monitors and polar orbiting satellites often have gaps in space and time that must be interpolated. Thus, new Gaussian process approximations are proposed that significantly reduce computational effort while improving approximations, allowing for fast and accurate interpolations. (2) Geostationary satellite sensors afford the opportunity for fine scale, continual monitoring of the atmosphere. This proposal outlines a framework for using these data--which consist of a temporal sequence of images--for the purpose of inferring upper air wind fields. (3) The pace of supercomputing has continued to increase our ability to produce high-resolution numerical simulations, which requires new computational tools for analyzing the output. A technique is proposed for local estimation that results in a globally valid statistical model, a critical feature that enables numerical model emulation and data compression via statistical models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.